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2-3 Slope Slope 4 indicates the steepness of a line. 4 is “the change in y over the change in x” (vertical over horizontal). 4 is the ‘m’ in y = mx + b.

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Finding the Slope of a Line 4 m = 4 m 4 We use the first equation when given a graph, the second when given a table, and the third when given two points.

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Slope 4 If a line rises from left to right (uphill), it has a positive slope. 4 If a line falls from left to right (downhill), it has a negative slope. x y x y

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Slope 4 If a line is vertical, it has an undefined slope. 4 If a line is horizontal it has a slope equal to 0. x y x y

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Find the Slope 4 To find the slope of this line we will use rise/run. 4 Pick either point. 4 We find the rise by counting up (+) or down (-). 4 Rise is 3 up from the bottom or -3 down from the top point. x y

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Find the Slope 4 To find the run, we count right (+) or left (-). 4 If you started from the top point, your run will be left -2, if you started at the bottom point, your run will be right 2. x y

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Find the Slope 4 So if you started with the top point, your slope would be -3/-2. 4 If you started with the bottom point, your slope would be 3/2. 4 Are these the same? Yes!! The slope of the line is 3/2. x y

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Find the Slope x y x y 4 m =

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Find the Slope 4 m= undefined x y x y 4 m = 0

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Find the Slope of the Line 4 Given the points (5, 1) & (6, 4) m = = = 3 4 Given the points (-6, -2) & (-1, 0) 4 m =

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Slope-Intercept Form y = mx + b [or f(x) = mx + b] m is the slope b is the y-intercept

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Find the Equation of the Line What is the y-intercept? b = -2 What is m? m = y = x -2 x y

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Find the Equation of the Line b = ? b = 1 m = ? m = - y = - x + 1 x y

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Find the Equation of the Line b = ? b = 4 m = ? m = 0 y = 0x+ 4 y=4 x y

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Find the Equation Given the Slope and y-intercept 1) m = -3, b = 1 y = -3x + 1 2) m = -, b = -4 y = - x - 4

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Find the Slope and y-intercept of each Equation: 1) y = -4x + 3 m = -4 b = 3 2) y = 5 - x m = - b = 5 3) 8x + y = m = -8 b = 4) 4x - 2y = 10 m = 2 b = -5

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Find the Equation Given the Slope and a Point Given m = -1, (2, 1) First, calculate b by substituting the slope and the coordinates into y = mx + b. y = -1x + b 1 = -1(2) + b 1 = -2 + b 3 = b y = -1x + 3

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Find the Equation Given Two Points Given (-1, 3) and (2, 1) First, calculate the slope: Second, find b. Use either point... m =, (2, 1) 1 = (2) + b 1 = + b = b

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Homework: 4 Graphing Linear Equations Worksheet (front and back)

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